You should only need the libqt6svg6 to fix the icon issue. And it's only a runtime requirement, so it can even be installed after building Sigil.
You don't need libqt6svg6-dev or libqt6svgwidgets6 to build or run Sigil.
The current Build_on_Linux.md file in the /docs folder on github should now have the complete list of qt6 dependencies needed to build and run Sigil on Debian/Ubuntu.
Code:
sudo apt-get install qt6-webengine-dev qt6-base-dev-tools qt6-tools-dev qt6-tools-dev-tools qt6-5compat-dev libqt6svg6
The above will pull in everything else needed.